Geodesic
A Note on Barnette’s Conjecture
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 133-137

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Barnette conjectured that each planar, bipartite, cubic, and 3-connected graph is hamiltonian. We prove that this conjecture is equivalent to the statement that there is a constant c gt; 0 such that each graph G of this class contains a path on at least c|V (G)| vertices.
Keywords: planar graph, Hamilton cycle, Barnette’s Conjecture 
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Harant, Jochen. A Note on Barnette’s Conjecture. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 133-137. http://geodesic.mathdoc.fr/item/DMGT_2013_33_1_a10/